The conjugacy classes of metabelian groups of order at most 24

Abstract

In this paper, G denotes a non-abelian metabelian group and cl(x) denotes conjugacy class of the element x in G. Conjugacy class is an equivalence relation and it partitions the group into disjoint equivalence classes or sets. Meanwhile, a group is called metabelian if it has an abelian normal subgroup in which the factor group is also abelian. It has been proven by an earlier researcher that there are 25 non-abelian metabelian groups of order less than 24 which are considered in this paper. In this study, the number of conjugacy classes of non-abelian metabelian groups of order less than 24 is computed.